Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the use in this Amendment No. 3 to the Registration Statement (No. 333-250945) on Form S-1 of KemPharm, Inc. of our report dated February 28, 2020, except for the Reverse Stock Split paragraph of Note A as to which the date is December 27, 2020, relating to the financial statements of KemPharm, Inc., appearing in the Prospectus, which is part of this Registration Statement.

We also consent to the reference to our firm under the heading “Experts” in such Prospectus.

/s/ RSM US LLP

Orlando, Florida

January 5, 2021